Acceleration, streamlines and potential flows in general relativity: analytical and numerical results

Analytical and numerical solutions for the integral curves of the velocity field (streamlines) of a steady-state flow of an ideal fluid with a p = rho equation of state are presented. The streamlines associated with an accele rate black hole and a rigid sphere are studied in some detail, as well as t he velocity fields of a black hole and a rigid sphere in an external dipola r field (constant acceleration field). In the latter case the dipole field is produced by an axially symmetric halo or shell of matter. For each case the fluid density is studied using contour lines. We found that the presenc e of acceleration is detected by these contour lines. To the best of our kn owledge this is the first time that the integral curves of the velocity fie ld for accelerated objects and related spacetimes have been studied in gene ral relativity.